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Dana Ernst

  • PhD Mathematics
  • Assistant Professor
  • Northern Arizona University
  • 1

    h-index

    Impact measure calculated by Scopus using these publications and citation counts.
  • 3

    Citations

    Number of citations received by these publications in Scopus.

Research interests

Kazhdan–Lusztig theory generalized Temperley–Lieb algebras Coxeter groups Hecke algebras diagram algebras inquiry-based learning (IBL) scholarship of teaching and learning (SoTL) combinatorial game theory impartial games

About

My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebras, Kazhdan-Lusztig theory, generalized Temperley-Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. More recently, my research has expanded into combinatorial game theory (joint with Nandor Sieben and Bret Benesh). In particular, our research has focused on avoidance and achievement games involving finite groups. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible. My interests also include the scholarship of teaching and learning (SoTL) with a focus on inquiry-based learning (IBL) as an approach to teaching/exploring mathematics. I am currently a Special Projects Coordinator for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom. Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too. For more information, see my webpage: http://dcernst.github.io.

Co-authors (12)

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Publications

Cominuscule elements of Coxeter groups of type affine $C$

  • Ernst D
  • Green R
In preparation (2016)
  • --

    Readers

    Readers not available. This publication is not currently accessible in the Mendeley catalog.

Conjugacy classes of cyclically fully commutative elements in Coxeter groups of type $A$

  • Ernst D
  • Fox B
In preparation (2016)
  • --

    Readers

    Readers not available. This publication is not currently accessible in the Mendeley catalog.

Impartial achievement and avoidance games for generating generalized dihedral groups

  • Benesh B
  • Ernst D
  • Sieben N
{\tt arXiv:1608.00259} (2016)
  • --

    Readers

    Readers not available. This publication is not currently accessible in the Mendeley catalog.

T-avoiding elements of Coxeter groups

  • Ernst D
  • Laird T
In preparation (2016)
  • --

    Readers

    Readers not available. This publication is not currently accessible in the Mendeley catalog.

The many faces of IBL

Handbook of Research on Pedagogical Practice in STEM Education (2015)
  • --

    Readers

    Readers not available. This publication is not currently accessible in the Mendeley catalog.

Professional experience

Assistant Professor

Northern Arizona University

August 2012 - Present

Assistant Professor

Plymouth State University

August 2008 - May 2012 (4 years)

Graduate Student

University of Colorado Boulder

September 2003 - August 2008 (5 years)

Faculty

Front Range Community College

September 2001 - May 2003 (2 years)

Graduate Teaching Assistant & Instructor

Northern Arizona University

August 1997 - May 2001 (4 years)

Education history

University of Colorado Boulder

PhD, Mathematics

September 2003 - August 2008 (5 years)

Northern Arizona University

MS, Mathematics

August 1997 - May 2000 (3 years)

George Mason University

BS, Mathematics

September 1993 - May 1997 (4 years)